Problem: $P(x)=x^4-2x^3-3x^2+4$ What is the remainder when $P(x)$ is divided by $(x-3)$ ?
Solution: We can use the polynomial remainder theorem to solve this problem: For a polynomial $p(x)$ and a number $a$, the remainder on division by $x-a$ is $p(a)$. According to the theorem, the remainder when $P(x)$ is divided by $(x-{3})$ is $P({3})$ : $\begin{aligned} P({3})&=({3})^4-2({3})^3-3({3})^2+4 \\\\ &=81-2 \cdot 27-3 \cdot 9+4 \\\\ &=4 \end{aligned}$ In conclusion, the remainder when $P(x)$ is divided by $(x-3)$ is $4$.